1. Field of the Invention
The present invention relates generally to computer aided manufacturing (CAM), and in particular, to a method, apparatus, and article of manufacture for spiral machining based on a suitable toolpath.
2. Description of the Related Art
(Note: This application references a number of different publications as indicated throughout the specification by reference numbers enclosed in brackets, e.g., [x]. A list of these different publications ordered according to these reference numbers can be found below in the section entitled “References.” Each of these publications is incorporated by reference herein.)
A fundamental problem often arising in the CAM industry is to find a suitable toolpath for milling a pocket that is defined by a shape in the plane. A computer numerical control (CNC) milling machine is programmed to follow the toolpath and thus cutting a cavity with the shape of the given pocket in a solid piece of material. The cutter of the machine can be regarded as a circular disc with radius r, and the task is to find a toolpath in the plane such that the swept volume of the disc, when the disc center is moved along the path, covers all of the pocket. One may assume for simplicity that the toolpath is allowed to be anywhere in the pocket.
Some work has been made on spiral toolpaths that morph a point within the pocket to the boundary of the pocket [3, 9, 2, 11, 10]. The method described by Held and Spielberger [9] yields a toolpath that (i) starts at a user-specified point within the pocket, (ii) ends when the boundary is reached, (iii) has no self-intersections, (iv) is G1 continuous (a plane curve is G1 continuous or tangent continuous if there exists a continuous and differentiable parameterization of the curve), (v) makes the width of material cut away at most δ at any time, where δ is a user-defined constant called the stepover. One must have δ<2r, since otherwise some material might not be cut away. Most traditional toolpath patterns have many places where the cutter does not cut away any new material, for instance in retracts where it is lifted and moved in the air to another place for further machining, or self-intersections of the toolpath, where the tool does not cut away anything new when it visits the same place for the second time. That may increase machining time and lead to visible marks on the final product. Spiral toolpaths have the advantage that the cutter is cutting during all of the machining and that, at the same time, the user can control the stepover. Spiral toolpaths are particularly useful when doing high-speed machining, where the rotational speed of the cutter and the speed with which it is moved along the toolpath is higher than in conventional milling. Held and Spielberger [9] provide a more detailed discussion of the benefits of spiral toolpaths compared to various other toolpath patterns and more information on CNC milling in general.
Bieterman and Sandstrom [3] and Huertas-Talón et al. [11] give methods for computing spiral toolpaths by solving elliptic partial differential equation boundary value problems defined on the pocket. However, the methods only work for star-shaped pockets [9] (a polygon is star-shaped if there exists a point p in the polygon such that the segment pq is contained in the polygon for every other point q in the polygon).
It is desirable to provide an alternative construction of spirals that also satisfy the previously mentioned properties of the construction of Held and Spielberger [9]. Held and Spielberger provide a method where the toolpath is generated by interpolating growing disks placed on the Voronoi diagram of the pocket. The union of the discs at a certain time represents the area machined at that time.